I managed to get a scene like this running in GB Studio (the framerate of the GIF might be worse than it originally was, but you get the idea) , so it can definitely be done, but there are a few caveats:
-As far as I understand it, you need to build the backgrounds in a separate program. I used Pyxel Edit, but there are others (even free ones).
-I personally also cut the player sprite into a separate file from the main image, but I'm not sure if that's necessary.
-Since the sprites were not built with GB Studio in mind, some sprites need to be simplified (like I did to my player sprite here) or split into multiple sprites to fit the 4-colors-per-sprite limitation. That, or let GB Studio pick a palette and not worry about the fact that it looks simpler than the original sprite. So scenes like my example images most likely cannot be built out of the box.
I barely understand anything about GB Studio, though, so take everything I just said with a grain of salt.